Topics: Starter | Area | Mensuration | Puzzles | Ratio | Shape

• David, Kawartha Pine Ridge District School Board
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• My main concern is that this references the shape as a right-triangle which neither is in actuality. I think this throws the students off a possible thinking path. If instead it referred to the shape less specifically, then students might more readily venture down this path.
• Transum,
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• Good point David. The phrase 'right-angled triangles' has now been replaced with the word 'shapes' in the text above. Thanks very much for the suggestion.
• Tara, Brisbane
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• Was trying to plan a good lesson for ratio. As a substitute teacher, putting together an engaging lesson is paramount to avert discipline issues. So thought it just perfect, in keeping with the first step of arousing the interest of the class. Thank you.
• H Rollo, Brechin High
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• Could be used for introducing gradient.
  
  [Transum: That is a very good idea. I too use the notion of gradient when getting students to analyse the situation.]
• Brandon, The Bronx
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• Cheating. The top triangle, measured as one unit has an area of 32.5. If we assume each cut up piece touches the grid, then we get get triangles of area: 12 (1/2* 8*3), 8, 7 and 5 (1/2 * 5*2) = 32. It doesn't matter what the bottom triangle looks like, the top triangle is lying to us and the bottom could be anything marginally different by not quite, but almost touching the grid lines anyway you'd like. Tricky. I like it becait tests our tacit assumption that the sub-shapes all touch the grid lines, when they don't.
• Berten Stan, Oxford High
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• Good activity,would like to see more.
• Ben Sparks, Twitter
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• Here's a classic 'Missing Square' dissection. The pieces don't change area. Where does the square come from? Attributed to Mitsunobu Matsuyama. Interactive @geogebra file here: https://t.co/ffBYXQYFYy pic.twitter.com/ZFLvsxzdda

  — Ben Sparks (@SparksMaths) February 27, 2021

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